Civil War Battles and Railroad Junction Proximities

Introduction

The US Civil War was one of the first wars that attempted to leverage the use of railroads. Controlling railroad locations and having easy access contributed to the Union’s ability to win the war, especially because most battles took place in the US South. Railroads are able to be utilized to transport troops and supplies, and by doing so provide crucial support for an army that is not on its home soil.

The question I would like to explore: Is the Union more likely to win battles that are located in close proximity to railroad junctions?

Null hypothesis: The likelihood that an Union victory occurs at the given point s_i is directly proportional to the density of railroad junctions at that point.

Alternative hypothesis: There exists a population density threshold _p^*_ such that Union victories occur at locations _s_i^*_ with railroad junction density greater than _p^*_ more often than what would be expected solely on the basis of this railroad junction density.

Broad Roadmap

Determine where the railroad junctions are located (specifically in the US South).
Determine where Civil War battles took place.
Analyze distances from battle sites to railroad junctions.
Compare intensity functions of railroad junctions and battle sites.
Run an experiment that randomizes some element of battle sites location or railroad junction locations.
Examine possible spatial effect of railroad junctions on the results of battles, specifically battles that resulted in an Union victory.
Is there anything we can test regarding the significance of the battle?

Exploratory Data Analysis (EDA)

library(tidyverse) |> suppressPackageStartupMessages()
library(sf) |> suppressPackageStartupMessages()
library(mapview) |> suppressPackageStartupMessages()
library(units) |> suppressPackageStartupMessages()
library(concaveman) |> suppressPackageStartupMessages()
library(dplyr) |> suppressPackageStartupMessages()
library(spatstat) |> suppressPackageStartupMessages()
cb_palette <- c("#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")

junction_df <- read_csv("Junction.csv", show_col_types = FALSE)

New names:
• `` -> `...4`

Warning: One or more parsing issues, call `problems()` on your data frame for details,
e.g.:
  dat <- vroom(...)
  problems(dat)

junction_df |> head()

X	Y	Name	…4
-85.38300	32.64540	Junction	NA
-81.96342	33.47022	Junction	NA
-77.05674	38.81042	Junction	NA
-90.04864	29.94394	Junction	NA
-81.31636	34.24344	Junction	NA
-76.79234	39.12509	Junction	NA

junction_sf <- junction_df |> sf::st_as_sf(
  coords=c("X","Y"),
  crs=4326
) |> sf::st_transform(3857)
mapview(junction_sf)

battle_df <- read_csv("nps_battles.csv", show_col_types = FALSE)
battle_df <- battle_df %>% 
  mutate(
    significance_numeric = case_when(
      significance == 'A' ~ 4,
      significance == 'B' ~ 3,
      significance == 'C' ~ 2,
      significance == 'D' ~ 1
    )
  )

battle_df |> head()

cwsac_id	battle_name	start_date	end_date	theater_code	campaign_code	result	cwss_url	partof_cwss	forces_text	casualties_text	results_text	preservation	significance	cwsac_url	other_names	partof_cwsac	cws2_url	study_area	core_area	potnr_boundary	partof_cws2	interpretive_combat_arm	interpretive_minority_troops	interpretive_joint_ops	significance_jim	significance_ed	significance_bill	aad_url	battle_type	partof_aad	lat	long	state	strength_mean	strength_var	casualties_kwm_mean	casualties_kwm_var	comment	significance_numeric
AL001	Day’s Gap	1863-04-30	1863-04-30	MW	MW63-03	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL001	TRUE	Men from 51st Indiana Infantry, 73rd Indiana Infantry, 3rd Ohio Infantry, 80th Illinois Infantry, and 1st Middle Tennessee Cavalry [US]; three regiments [CS]	88 total (US 23; CS 65)	Union victory, although the raid ultimately failed.	III.3	C	http://www.nps.gov/abpp/battles/al001.htm	Sand Mountain	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	5410.35	1084.76	2933.02	TRUE	1	0	0	NA	D	C	http://aad.archives.gov/aad/record-detail.jsp?rid=320&dt=295	Action	TRUE	34.3096	-87.0110	AL	NA	NA	88	0.1666667	NA	2
AL002	Athens	1864-01-26	1864-01-26	MW	MW64-02	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL002	TRUE	9th Illinois Mounted Infantry [US]; 1st Alabama Cavalry [CS]	50 total (US 20; CS 30)	Union victory (The Confederate force failed in its attempt to take Athens.)	IV.1	D	http://www.nps.gov/abpp/battles/al002.htm	NA	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	21919.82	2274.85	2998.41	TRUE	0	0	0	NA	D	NA	http://aad.archives.gov/aad/record-detail.jsp?rid=314&dt=295	Attack	TRUE	34.8033	-86.9722	AL	800	1666.667	50	16.6666667	NA	1
AL003	Mobile Bay	1864-08-02	1864-08-23	MW	MW64-09	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL003	TRUE	Farragut’s Fleet (14 wooden ships and 4 monitors) and U.S. army forces near Mobile [US]; Buchanan’s Flotilla (3 gunboats and an ironclad), Fort Morgan Garrison, Fort Gaines Garrison, and Fort Powell Garrison [CS]	1,822 (US 322; CS 1,500)	Union victory	I.1	A	http://www.nps.gov/abpp/battles/al003.htm	Passing of Forts Morgan and Gaines	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	36916.74	16130.48	34927.42	TRUE	0	0	1	NA	NA	NA	http://aad.archives.gov/aad/record-detail.jsp?rid=323&dt=295	Naval Operations	TRUE	30.2410	-88.0530	AL	NA	NA	1827	833.4166667	NA	4
AL004	Decatur	1864-10-26	1864-10-29	MW	MW64-13	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL004	TRUE	Garrison and other troops sent there (approx. 5,000 men) [US]; Army of Tennessee [CS]	605 total (US 155; CS 450)	Union victory (Confederate forces could not cross the river.)	IV.2	C	http://www.nps.gov/abpp/battles/al004.htm	NA	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	14623.51	1148.87	0.00	TRUE	0	0	0	NA	C	NA	http://aad.archives.gov/aad/record-detail.jsp?rid=3&dt=295	Demonstration	TRUE	34.6140	-86.9860	AL	NA	NA	355	833.4166667	NA	2
AL005	Spanish Fort	1865-03-27	1865-04-08	MW	MW65-02	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL005	TRUE	XVI and XIII Corps [US]; Spanish Fort Garrison [CS]	1,401 (US 657; CS 744)	Union victory	IV.2	B	http://www.nps.gov/abpp/battles/al005.htm	NA	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	3742.16	2282.27	0.00	TRUE	0	0	0	NA	B	C	http://aad.archives.gov/aad/record-detail.jsp?rid=2&dt=295	Siege & Capture	TRUE	30.6843	-87.9164	AL	NA	NA	1398	0.1666667	NA	3
AL006	Fort Blakely	1865-04-02	1865-04-09	MW	MW65-02	Union	http://www.nps.gov/civilwar/search-battles-detail.htm?battleCode=AL006	TRUE	XIII and XVI Corps [US]; Fort Blakely Garrison [CS]	Total 4,475. April 9 only 3,529 (US 629; CS 2,900)	Union victory (Fort Blakely surrendered.)	III.1	A	http://www.nps.gov/abpp/battles/al006.htm	NA	TRUE	http://www.nps.gov/abpp/CWSII/CWSACReportAlabamaUpdate.pdf	6061.92	3743.28	4640.71	TRUE	0	1	0	B	A	B	http://aad.archives.gov/aad/record-detail.jsp?rid=1&dt=295	Siege & Capture	TRUE	30.7424	-87.9270	AL	20000	166666.667	4475	833.4166667	NA	4

battle_sf <- battle_df |> sf::st_as_sf(
  coords=c("long","lat"),
  crs=4326
) |> sf::st_transform(3857)
mapview(battle_sf,zcol="result", label="result")

battle_sf_significance <- battle_df |> sf::st_as_sf(
  coords=c("long","lat"),
  crs=4326
) |> sf::st_transform(3857)
mapview(battle_sf_significance,zcol="result", cex="significance_numeric", label="result")

Hypothesis Testing

Let’s generate a sample that randomly assigns the outcome of the battle.

battle_sf_sample <- battle_df |> sf::st_as_sf( coords=c("long","lat"), crs=4326
) |> sf::st_transform(3857)
N <- 300
battle_sf_sample <- battle_sf_sample |> sample_n(N) |> 
  mutate(label = paste0("Result: ",result))
mapview(battle_sf_sample,zcol="result", label="result")

Making a hull for the junctions.

hull_sf <- battle_sf |>
  concaveman::concaveman(concavity=3) |>
  sf::st_buffer(dist=5)
plot(hull_sf)

Making a ppp object for the junctions.

junction_sfc <- junction_sf |> sf::st_as_sfc()
junction_ppp <- as.ppp(junction_sfc, W=as.owin(hull_sf))

Warning: 5 points were rejected as lying outside the specified window

plot(junction_ppp)

Warning in plot.ppp(junction_ppp): 5 illegal points also plotted

battle_sfc <- battle_sf |> sf::st_as_sfc()
battle_ppp <- as.ppp(battle_sfc, W=as.owin(hull_sf))

Warning: data contain duplicated points

plot(battle_ppp)

Intensity functions

junction_int <- density(junction_ppp)
plot(junction_int)

battle_int <- density(battle_ppp)
plot(battle_int)

Observed quadrant counts

num_regions <- 3
region_labels <- c("Low", "Medium", "High")
junction_vals <- junction_int
junction_quant <- quantile(junction_vals, probs=(0:num_regions)/   num_regions, na.rm=TRUE) 
junction_cut <- cut(junction_vals, breaks=junction_quant, labels=region_labels)
junction_areas <- tess(image=junction_cut)
plot(junction_areas)

union_sf <- battle_sf |> filter(result == "Union") 
union_sfc <- union_sf |> sf::st_as_sfc() 
union_ppp <- as.ppp(union_sfc, Window(junction_ppp))
plot(union_ppp)

obs_union_counts <- quadratcount(union_ppp, tess=junction_areas) |> as.vector() 
names(obs_union_counts) <- region_labels
obs_union_counts

   Low Medium   High 
     9     41    144

Monte Carlo pipeline

set.seed(1007)
gen_sim_ppp <- function() {
  union_sim <- spatstat.random::rpoint( n = nrow(union_sf),
  f = junction_int
)
  return(union_sim)
}
sim_union_ppp <- gen_sim_ppp() 
plot(sim_union_ppp)

compute_quadrat_counts <- function(sim_ppp) {
  sim_counts <- quadratcount(sim_ppp, tess=junction_areas) |> as.vector() 
  names(sim_counts) <- region_labels
  return(sim_counts)
} 
compute_quadrat_counts(sim_union_ppp)

   Low Medium   High 
     0     24    170

set.seed(1007)
gen_sims_ppp <- function(num_sims) {
  union_sims <- spatstat.random::rpoint( n = nrow(union_sf),
  f = junction_int,
  nsim = num_sims
)
return(union_sims) }

full_sims_list <- gen_sims_ppp(num_sims = 999)
full_sim_area_counts <- lapply(X=full_sims_list, FUN=compute_quadrat_counts) 
full_count_df <- as_tibble(full_sim_area_counts) |> t() |> as_tibble()

Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if
`.name_repair` is omitted as of tibble 2.0.0.
ℹ Using compatibility `.name_repair`.

colnames(full_count_df) <- region_labels 
full_count_df |> head()

Low	Medium	High
0	24	170
2	28	164
0	25	169
1	20	173
1	30	163
2	27	165

Test statistic

mc_df <- bind_rows(full_count_df, obs_union_counts)

full_count_df |> ggplot(aes(x=High)) +
  geom_density(fill=cb_palette[2], alpha=0.5) + 
  geom_vline(xintercept = obs_union_counts["High"], linetype="dashed", color=cb_palette[1])

p_value_df <- mc_df[mc_df$High <= obs_union_counts["High"],] 
p_value <- nrow(p_value_df) / nrow(mc_df) 
p_value

[1] 0.001

What about Confederate victories?

confed_sf <- battle_sf |> filter(result == "Confederate") 
confed_sfc <- confed_sf |> sf::st_as_sfc() 
confed_ppp <- as.ppp(confed_sfc, Window(junction_ppp))

Warning: data contain duplicated points

plot(confed_ppp)

obs_confed_counts <- quadratcount(confed_ppp, tess=junction_areas) |> as.vector() 
names(obs_confed_counts) <- region_labels
obs_confed_counts

   Low Medium   High 
     1     27     92